An implicit kinetic inviscid flux for predicting continuum flows in all speed regimes

TL;DR

This paper improves the kinetic inviscid flux (KIF) method by developing an implicit strategy and a new weighting scheme, enhancing accuracy and stability across all flow regimes, especially in shock and boundary layer problems.

Contribution

It introduces an implicit coupling of KIF with a new weighting scheme combining KFVS and TTT methods, enabling larger CFL numbers and improved accuracy in all speed regimes.

Findings

Enhanced accuracy in shock and boundary layer simulations.

Ability to use larger CFL numbers without stability loss.

Validated across six diverse flow cases.

Abstract

In this study, the kinetic inviscid flux (KIF) is improved and an implicit strategy is coupled. The recently proposed KIF is a kind of inviscid flux, whose microscopic mechanism makes it good at solving shock waves, with advantages against the shock instability phenomenon. When developing the implicit KIF, a phenomenon is noticed that the kinetic flux vector splitting (KFVS) part in boundary layers not only reduces the accuracy, but seriously reduces the Courant-Friedrichs-Lewy (CFL) number as well. As a result, in this paper, a new weight is proposed about how to combine the KFVS method well with the totally thermalized transport (TTT) method. Besides admitting the using of larger CFL numbers, this new weight brings about more accurate numerical results like pressure, friction coefficient and heat flux when solving shock waves, boundary layers and complex supersonic/hypersonic flows. In order to examine the validity, accuracy and efficiency of the present method, six numerical test cases, covering the whole speed regime, are conducted, including the hypersonic viscous flow past a cylinder, the hypersonic double-cone flow, the hypersonic double-ellipsoid flow, the laminar shock boundary layer interaction, the supersonic flow around a ramp segment and the lid-driven cavity flow. The advantages of this scheme and corresponding mechanisms are to be discussed in detail.